MASTER'S THESIS. Cumulative Effects of Micrometeoroid Impacts on Spacecraft. Lei Zhao. Luleå University of Technology

Transcription

1 MASTER'S THESIS 2010:037 Cumulative Effects of Micrometeoroid Impacts on Spacecraft Lei Zhao Luleå University of Technology Master Thesis, Continuation Courses Space Science and Technology Department of Space Science, Kiruna 2010:037 - ISSN: ISRN: LTU-PB-EX--10/037--SE

2 CRANFIELD UNIVERSITY LEI ZHAO CUMULATIVE EFFECTS OF MICROMETEOROID IMPACTS ON SPACECRAFT SCHOOL OF ENGINEERING MSC in Astronautics and Space Engineering (SpaceMaster) MSc Thesis

3 CRANFIELD UNIVERSITY SCHOOL OF ENGINEERING MSc in Astronautics and Space Engineering (SpaceMaster) MSc Thesis Academic Year LEI ZHAO CUMULATIVE EFFECTS OF MICROMETEOROID IMPACTS ON SPACECRAFT Supervisor: Dr. S. E. Hobbs June 2010 This thesis is submitted in partial (45%) fulfilment of the requirements for the degree of Master of Science c Cranfield University All rights reserved. No part of this publication may be reproduced without the written permission of the copyright owner.

4 Abstract Abstract The geostationary orbit (GEO), which is an ideal orbit for communication and earth observation satellites, is accumulating an increasing number of spacecraft. Lack of atmospheric drag keeps the retired satellites near GEO orbit extremely long. Therefore it is interesting and meaningful to know the long-term effects of micrometeoroid impacts on spacecraft. This thesis aims to study the cumulative effects of micrometeoroid impacts on spacecraft in GEO and quantify the timescale for them to damage the typical spacecraft surface materials that are currently widely used in space missions. The mechanism of hypervelocity impact by a single particle is thoroughly reviewed and a set of damage scaling equations are chosen to evaluate the damage of single micrometeoroid impact. In combination with the implementation of the interplanetary meteoroid flux model developed by Grün et al., the cumulative effects of micrometeoroid impacts on cover glass of solar cells, MLI and radiators are quantified in terms of Volume Ejection Rate (VER) and Area Damage Rate (ADR). Furthermore a simple model is developed to predict the probability of a catastrophic collision between a meteoroid particle and a spacecraft. The results from both long-term effects and catastrophic collision are discussed and compared. The results show that it takes about several 10 4 years for micrometeoroid impacts to erode away the cover glass material and radiator material, or cover all the MLI surface area, and that after 100 years the chance of a catastrophic collision that can totally fragment the impact target is about one impact per 10 5 years. According to the study herein only re-orbiting spent GEO satellites to graveyard orbit is not a sustainable enough solution in the long term. I

5 Acknowledgements Acknowledgements The thesis would not have been finished without support from many people. First I would like to thank my family for their constant support and understanding during my study. I would also like to thank Dr. James Campbell for talking with me about his work on hypervelocity impacts and suggestions for my project. I want to express my thanks to my mates Campbell Pegg, Abrar Blauch, Karolina Johansson, and Lin Gao for their support. I would also like to particularly thank my dear friends Cheng Cheng and Wang Meng for providing me very comfortable and quiet places to write my thesis. Finally I wish to thank my supervisor, Dr Steve Hobbs, for his kindness and advices during the whole project. II

6 Table of Contents Table of Contents Abstract... I Acknowledgements... II Table of Contents... III List of Figures... V List of Tables... VI List of Notation... VII 1. Introduction Background Project aims and objectives Outline of the report Literature review Space debris and meteoroid environment Space debris Meteoroids Micrometeoroid flux models Grün et al. model The Divine/Staubach model ESA MASTER Hypervelocity impact Impact effects Ground testing facilities and in situ impact detector Impact features Impact damage equations Spacecraft structure analysis Summary Methodology Single Impact Micrometeoroid flux Cumulative effects Analysis of different exposed surfaces III

7 Table of Contents 4.1 Solar Cells Solar cell structure Single impact damage on solar cells Cumulative damage Lifetime estimates Multi-Layer Insulation (MLI) Structure of MLI Single impact on MLI Cumulative damage Lifetime estimates Radiator Structure of radiator Single impact on radiator surface Cumulative damage Lifetime estimate Summary Results and Discussions Long-term effects of micrometeoroid environment Probability of a catastrophic collision GEO spacecraft evolution Cumulative flux The probability Comparison of catastrophic collision and long-term erosion Uncertainties and errors Cumulative damage model Catastrophic collision prediction model Conclusions References Appendix A this is a validation of the Matlab function which implements the Grün et al. model 46 Appendix B Program for calculation of ballistic limit Appendix C - Programs for quantification of cumulative effects Appendix C1: Cumulative_damage_cover_glass.m Appendix C2: Cumulative_damge_MLI.m Appendix C3: Cumulative_damage_radiators.m Appendix C4: Integral functions IV

8 List of Figures List of Figures Figure 1 Polar view of objects in LEO and Geosynchronous orbit (NASA Orbital Debris Program Office, 2009) Figure 2 Illustration of a Van De Graaff Accelerator (Burchell et al., 1999) Figure 3 Illustration of the light gas gun (Burchell et al., 1999) Figure 4 Hypervelocity impact on an aluminium plate (ESA, 2006) Figure 5 Hypervelocity impact on a brittle material (ESA, 2006)(ESA, 2006) Figure 6 Measured parameters of impacts on solar cell surfaces (ESA, 2006) Figure 7 The structure of solar cells on EuReCa (ESA, 2006) Figure 8 The typical structure of MLI (Turner et al., 2001) Figure 9 Detailed composition of a typical MLI blanket. (Wertz and Larson, 2003) Figure 10 The hole observed on one of Atlantis orbiter s radiator panel. (Oberg, 2006) V

9 List of Tables List of Tables Table 1 Summerization of typical spacecraft surface areas Table 2 the material properties and geometry features of micrometeoroids and cover glass (ESA, 2006) 23 Table 3 Calculation process and formula of VER and ADR regarding the cover glass Table 4 Formula to estimate lifetime of cover glass and results Table 5 the material properties and geometry features of micrometeoroids and the first layer of MLI blanket Table 6 Calculation process and formula of ADR regarding the cover layer of MLI blanket Table 7 Material properties and geometry features of micrometeoroids and radiators Table 8 Calculation process and formula of VER and ADR regarding the radiator Table 9 Formula to estimate lifetime of cover glass and results Table 10 Summarization of damage rates and lifetime estimates regarding cover glass, MLI, radiators respectively Table 11 Comparison of interplanetary meteoroid flux between calculated values and historical values(grün et al., 1985) VI

10 List of Notation List of Notation F s r 1 N A total m c M P T t Diameter of crater Diameter of perforation hole Diameter of impacting particles Diameter of conchoidal fracture zone Thickness of impacted target Marginal diameter of impacting particles Particle mass at marginal diameter Mean velocity of impacting micrometeoroids Cumulative flux of interplanetary micrometeoroids Derivative of cumulative flux Ejected target volume due to particles with a mass Damage area on the target surface due to particles with a mass Density of impacting particles Density of impacted targets Mean impacting angle Speed of sound in the projectile Speed of sound in the target Thickness of the target The relative impact velocity The angular sensitivity of the detector Scale factor Auxiliary variables The perihelion distance number of spacecraft Total exposed area of spacecraft Critical mass Mass of spacecraft Probability of a catastrophic collision Time unit Period of a catastrophic collision VII

11 1. Introduction 1. Introduction 1.1 Background Since the first man-made satellite was launched into space in 1957, an increasing number of spacecraft have been sent to Earth orbit. At that time the issue of orbital debris polluting the near-earth space was not addressed. Space is big, but in fact not as big as we thought several decades ago. Today the issue of space junk cannot be ignored any more. Scientists and engineers advocate sustainable use of Earth orbits, and suggested several measures to reduce the amount of orbital debris (Anselmo and Pardini, 2004; Johnson and Stansbery, 2010). Among the most effective methods is the end of life disposal which has been achieved in LEO, but still has not been implemented in GEO due to the larger efforts and cost. Satellites and orbital junk in GEO orbit are relatively stable comparing with those in LEO, for example they could stay in orbit for thousands of years but those in LEO orbit could re-enter the Earth s atmosphere due to atmospheric drag effects after hundreds of years. Lack of atmospheric drag makes the GEO orbit naturally vulnerable to pollution by orbital debris. If the orbit is polluted it can hardly be recovered by itself, leaving no effective way available to reduce the orbital debris in GEO. Therefore the issue becomes: how to dispose of end-of-life satellites in GEO and how they will evolve in the long term. Spacecraft in space are under the danger presented by meteoroids which could collide with them at velocities up to 100 km/s. The effects of hypervelocity impacts of meteoroids were investigated since 1960s due to the requirement of spacecraft protection and shielding. But, very limited knowledge of cumulative effects of meteoroid impacts on them has been obtained. Since the lifetime of spacecraft in GEO can be extremely long, it is quite interesting to study how the spacecraft in GEO will evolve under meteoroid impacts after thousands of years or even millions of years. 1

12 1. Introduction 1.2 Project aims and objectives The project aims to study the cumulative effects of micrometeoroid impacts on spacecraft in GEO orbit and to estimate the time scale for them to damage the typical surface of spacecraft. The objectives are as stated below: Review the current knowledge and understanding of orbit debris and the meteoroid environment, and determine a quantitative model of the particulate flux. Look into the damage mechanisms of how a single impact will impair the target. Develop a long-term damage model to quantify the cumulative effects of micrometeoroid impacts on spacecraft. Analyze the results and draw conclusion of the project. 1.3 Outline of the report This thesis will analyze the micrometeoroid environment in space, evaluate the risk of single catastrophic impacts and then quantify the cumulative effects of micrometeoroid impacts on spacecraft. Chapter 2 reviews current space debris and the micrometeoroid environment, micrometeoroid flux models, mechanisms of hypervelocity impacts and their damage to spacecraft, and the typical spacecraft structure that is exposed directly to the hypervelocity particulate environment. Chapter 3 presents the methodology of quantifying the cumulative effects of micrometeoroid impacts on spacecraft. Firstly, the mechanism of single impact and its damage effect on the target is addressed; then the micrometeoroid flux is implemented in the analytical model; finally, the cumulative effects of impacts quantified. Chapter 4 analyzes three different exposed structure surfaces including Solar Cells, Multi-Layer insulation and Radiators. Their structures are reviewed first, and then single impact on each target and cumulative damage due to micrometeoroid impacts are calculated, and the lifetime of each structure is given according to the calculation. Chapter 5 summarizes the results of analysis and discusses their implications. Chapter 6 gives the conclusions of the report. 2

13 1. Introduction Several appendices are included providing the supporting information of the study, for example the justification of the micrometeoroid flux model and programs to quantify the cumulative effects of micrometeoroid impacts. 3

14 2. Literature review 2. Literature review The project aims to improve understanding of the cumulative effects of hypervelocity impacts on spacecraft. This literature review gives an overview of relevant fields to the project objectives. It starts from the space debris and meteoroid environment, and then pays particular attention to the micrometeoroid flux models that are currently used and trusted in space industry. Furthermore, the mechanisms of hypervelocity impacts are surveyed thoroughly including the impact effects, ground testing facilities and in situ detectors, impact damage features and impact scaling laws. In the end the typical spacecraft surfaces are analyzed and quantified in terms of area. 2.1 Space debris and meteoroid environment Man-made space debris and natural meteoroids particles pose threats to spacecraft on orbit. In the beginning of space era only meteoroids were taken into account with respect to protection and shielding from hypervelocity particles. But at the moment the artificial satellites, to some extent, can no longer be ignored when planning a space mission. The particulate environment of space debris and micrometeoroids are reviewed in the following sections Space debris Space debris, also called orbital debris or space junk, refers to any object brought to space by humans that doesn t function any more. It consists of defunct spacecraft, upper stage rockets, products of collisions and explosions, and even lost equipment during human activities in space. Current situation According to NASA Orbital Debris Program Office s database (2009), there are currently about objects with sizes larger than 10 cm, tens of millions particulates smaller than 1 cm and about particles in between. The population of space debris is increasing continuously as more and more space missions have been launched to space. Regarding the orbits that space debris resides, it can be seen clearly, from NASA s illustration graphics Figure 1, which visualizes all the objects that are being monitored by the agency (95% 4

15 2. Literature review are space debris), that there exists two obvious belts where space debris most resides: the LEO orbit and the Geosynchronous Orbit, which are the most useful orbits for space missions. Basically the lifetime of space debris depends on the height of their orbits; the higher the orbit is, the longer they will stay. Debris in the LEO orbit normally will decay in several years to decades due to the atmospheric drag effects, while debris in GEO will stay in orbits for extremely long time, because there is no force pulling them back to the Earth. Currently all the spacecraft that have been sent to GEO orbit are either remain in their origin orbits or disposed to the grave yard orbit. It means that they will stay there until they are completely fragmented or destroyed by the surrounding environment. This is one of the reasons why the cumulative long-term effects of micrometeoroid impacts on spacecraft are of interest to be studied in this paper. Figure 1 Polar view of objects in LEO and Geosynchronous orbit (NASA Orbital Debris Program Office, 2009). 5

16 2. Literature review Debris flux model Since the environment of space debris can no longer be ignored for mission planning, it is necessary to develop a flux model which can quantify the population of current orbiting debris and which is also able to predict future debris environment. There are currently several models available and applicable to mission design, such as NASA s EVOLVE the NASA s ORDEM2000, the ESA s CHAINEE, and the UK s IDES and so on (Jehn et al., 1997). Since the impacts of space debris are not discussed in this paper, models of space debris are not reviewed in details. Debris mitigation If the concept of sustainable use of space is not implemented in future missions, the accumulation of space debris will make the orbits unusable after a period of time. Here ESA s mitigation strategies are summarized (Rex et al., 1999). They include: Passivation of spacecraft and upper stages at end of life. De-orbiting strategies. Re-orbiting of spacecraft to grave yard zone. Collision avoidance and shielding technology Meteoroids In contrast to the space debris environment, the meteoroid environment originates from natural environment, either from cometary sources or asteroidal sources. They are travelling with a high speed in the interplanetary space. Grün et al. (1985) summarized the general characteristics of meteoroids, among which the most important ones are the density of meteoroids, and the travelling speed, because the type and extent of damage features largely depend on the size, density, and speed of impacting particles. The former study and observations showed that 20% to 40% meteoroids have low densities about <1g/cm 3, whilst most of meteoroids have densities about 2.0 to 3.0 g/cm 3 ; accordingly, the author suggested an effective density of 2.5 g/cm 3. The meteoroid speed relative to the spacecraft presents a distribution in the range of 8 km/s up to 100 km/s as a function of particle mass. When the author developed the meteoroid flux model, the average speed was assumed as 20 km/s. 6

17 2. Literature review Since the interest of the thesis is to quantify the cumulative effects of meteoroids impacts, the flux of meteoroids is of particular importance to the study. The currently available flux models are reviewed specially in the following section. 2.2 Micrometeoroid flux models It is important to develop a quantitative micrometeoroid flux model to predict damage that space particles will cause on space missions and the collision possibilities of catastrophic impact. Currently there are several models available to evaluate micrometeoroids and orbital debris environment. They are usually developed on the basis of ground-based experiments and observations, in situ experiments, and observations. The following section reviews several models which are widely used in the community of science and engineering, and space agencies as well Grün et al. model Grün et al. (1985) developed a simple interplanetary micrometeoroid flux model, which has been used for modelling the micrometeoroid environment at 1AU for two decades and is still trusted in the space community. It was derived from some certain theoretical assumptions and was fitted to the data collected from in situ space impact detectors including the lunar cratering record, Pegasus, Explorer 16 and 23, HEOS 2 and Pioneer 8 and 9. The model gives an average cumulative flux of micrometeoroids (impacts per second per unit area due to particles with mass m and greater) onto a turning flat plate under a viewing angle of 2π sr at 1 AU. It assumes the flux is isotropic without any directional information. If the flux is defined as F, the flux intensity would be F/π, this is because the effective viewing angle is π sr rather than 2π sr. The standard cumulate flux is given in the following simple analytical equation: Where m is the particle mass in the unit of gram, c 4 ~c 10, ~ are all constants. The values of coefficients are, c 4 = , c 5 =15, c 6 = , and c 7 = , c 8 = , c 9 = , c 10 = , the exponents are =0.306, =-4.38, = 2, =4, and = -0.36, = 2, = (Grün et al., 1985). 7

18 2. Literature review The first bracket gives the contribution of large particles with mass greater than 10-9 g, the middle one carries the information of medium-size particles of mass between and 10-9, and the third part describes the flux of small particles with mass smaller than Note, the model requires an assumed meteoroid density of 2.5 g/cm 3, and a mean velocity of 20 km/s. The applicable mass range is assumed between and 10 2 g. In this paper the mass range is extrapolated to bigger particles of 10 3 g, with a compromise assuming it will not influence the accuracy too much. To expand the applicability of the Grün et al. model to LEO environment, an enhanced meteoroid model is derived by McDonnell et al. (1999) on the shoulder of Grün et al. model and in situ impact data from EuReCa and LDEF. It is found that the flux of total particles is not isotropic near the Earth due to the orbital debris that cannot be ignored any more, and that the flux is biased towards the Earth-apex direction The Divine/Staubach model Divine (1993) suggested a new concept of five population and developed a new meteoroid flux model based on his assumption. The author incorporated new data sets, including observations of radar meteoroids, in situ impact detectors onboard of Pioneer 10 and 11, Helios 1, Galileo and Ulysses. In addition, one of the five populations -the interplanetary flux used the Grün et al. model to estimate meteoroid flux near the Earth at 1 AU. The five sets of distributions are comprised of the asteroidal population, the core population, the halo population, the inclined population and the eccentric population. For details about how the different populations are defined refer to Staubach and Grün (1995). The Divine model is applicable to meteoroid flux in the heliocentric distance of 0.1 AU and 20 AU and the particle mass range between g and 1g. The analytical equation is: Where is the relative impact velocity, is the angular sensitivity of the detector and is a scale factor, and the auxiliary variables and are functions of the perihelion distance r 1, expressed as: 8

19 2. Literature review Staubach and Grün (1995; 1996) upgraded the Divine meteoroid flux model, and applied the model to calculate the fluxes onto satellites orbiting around the Earth accounting for both gravitational focusing and shielding of the Earth. Staubach (1997) presented the upgraded model, which implemented new factors: interstellar meteoroids discovered by the spacecraft Galileo and Ulysses, pressure caused by solar radiation affecting particles of masses lower than g.the flux onto spacecraft was calculated using the newly developed model and compared with data obtained from recent in situ measurements on LDEF, EuReCa, and HST solar arrays ESA MASTER 2001 MASTER (referring to the abbreviation of Meteoroid and Space Debris Terrestrial Reference Model) is a software application, which was developed by ESA (2006), aiming to characterize the environment of man-made orbital debris and meteoroids, and to evaluate their correspondent effects on space missions. The model was derived on the basis of semi-deterministic analysis and prediction techniques. Data of orbital debris is from several fragmentation experiments and integration of the current orbital debris sources. With respect to meteoroids the model developed by Divine (1993) and Staubach (1996) was implemented to the software. The model has the capability of providing a 3D description of particle distribution from LEO up to GEO region. 2.3 Hypervelocity impact Hypervelocity impact is defined when the impacting velocity is higher than the intrinsic speed of compression waves in the materials of both the impacting particle and the target. Normally they will be reached when the impacting speed is around several km/s; accordingly it is common to name any impact with speed higher than 2~3 km/s a hypervelocity impact. Hypervelocity impact phenomena have very close links with space missions, because objects in space all move in a high speed. With respect to space debris in low earth orbit the average impact velocity is 9.5 km/s and for interplanetary micrometeoroids the mean velocity is about 20km/s (McDonnell, 1999). The meteoroid particle with a mass of 4g travelling in speed of 20 km/s has 9

20 2. Literature review the equivalent kinetic energy with a 2 tons car running in a speed of 100kph, which is more than enough to cause severe damage to the spacecraft. Therefore, it is important to understand and quantify the hypervelocity impact mechanisms in order to have enough confidence in the survivability of spacecraft, at least to know how much risk the space mission will have with respect to possible failure caused by hypervelocity impacts by particles travelling in space Impact effects Drolshagen (2001) reviewed the hypervelocity impact effects that might happen on spacecraft. Effects caused by impacts from either interplanetary meteoroids or from orbital junks are nearly the same; hence impact effects discussed here are suitable for both types of hypervelocity particulates. In this paper the cratering and ejecta are of particular importance to the study. Basically, the effects include cratering and ejecta, structural damage, the generation of impact plasma, and momentum transfer. Cratering and ejecta Surface erosion and degradation leading to a change in thermal, optical or electrical properties. Degradation of sensors and mirrors, including impacts on internal instruments by secondary ejecta. Degradation of windows used. Sealing problems. Structural damage Penetration of spacecraft walls, leading to structural damage of inner subsystems. Penetration of pressurised vessels (tanks, manned modules, coolant loops). Cutting of cable or tether. Short circuits. Complete destruction of impacted spacecraft or spacecraft subsystem by larger object. Impact plasma The generation of plasma is basically because of the partial ionization of the particle and the target surface due to the extreme condition such as very high temperature and pressure during the hypervelocity impact. Electrical interference 10

21 2. Literature review Current flow. Triggering of electrostatic discharges. Light flashes Momentum transfer The momentum exchange can alter the attitude of spacecraft. (Drolshagen, 2001) Ground testing facilities and in situ impact detector During the last decades the research of applications of hypervelocity impact to space missions is mainly divided into two streams: ground-based testing and in situ investigation. There are several ground testing facilities that have been developed and generated plenty of useful impacting data, mainly located in US, Russia and Europe (Stilp, 1987). With respect to space impact detectors several space missions were launched to study the particle environment in space, such as LDEF, EuReCa and retrieved HST solar arrays. Ground testing facilities Burchell et al. (1999) reviewed two types of ground-based facilities: the Van De Graaff Accelerator to accelerate small dust particles less than one micron in size and the two-stage light gas gun to accelerate particles in the size range of 0.02 mm to 2 mm. They were developed at the University of Kent at Canterbury and the Open University in UK. Other facilities adopting the same techniques were also built at Ernst-Mach-Institute (EMI) and Technical University Munich (TMU) in Germany (Schäfer et al., 2001) and at Johnson Space Centre (NASA, 2006; Schonberg, 1999). The Van De Graaff Accelerator The basic design principle is to charge the dust particle first and then to increase its speed by a large potential field. The detailed design and specification is summarized by Burchell et al. (1999). With relevance to micrometeoroid impacts, the particles that are accelerated by Van De Graaff Accelerators are required to have dimension about microns and velocities in 1~50 km/s. A schematic diagram of a Van De Graaff Accelerator is shown in Figure 2. 11

22 2. Literature review Figure 2 Illustration of a Van De Graaff Accelerator (Burchell et al., 1999). Two-stage light gas gun The light gas gun allows particles in the size range of millimetre and centimetre to be accelerated to a speed of several km/s. Details of the design and operations could be found in Burchell et al. (1999) as well. The basic mechanism is to give an initial acceleration by burning a powder charge to the piston which is used to compress a light-molecular gas, when it is released the energy of expansion is then used to accelerate particles, hence the two-stage light gas gun. Figure 3 shows the schematic diagram of a light gas gun. Figure 3 Illustration of the light gas gun (Burchell et al., 1999). In situ impact detector in space To investigate the distribution of orbital debris and micrometeoroids near the Earth and their hazards to the spacecraft from hypervelocity impacts, it is of particular interest to launch in situ impact detector to space. Data from such missions as Pegasus, Explorer 16 and 23, HEOS 2, Pioneer 8 and 9, LDEF, EuReCa and HST solar arrays etc. provided very important information to derive the interplanetary micrometeoroid flux, distribution of orbital debris and damage features. 12

23 2. Literature review Grün et al. (1985) incorporated the lunar cratering record data, impact detector data from several spacecraft, including Pegasus, Explorer 16 and 23, HEOS 2 and Pioneer 8 and 9, to develop the interplanetary micrometeoroid flux at 1AU. Divine (1993) took impact detector data from Pioneer 10 and 11, Helios 1, Galileo and Ulysses into account and on the basis of the Grün et al. model the author developed an updated micrometeoroid flux model which was adopted by ESA MASTER (Meteoroid and Space Debris Terrestrial Environment Reference Model) 2001 model. It was compared with measured flux determined from in situ spacecraft measurements including LDEF, EuReCa, and HST retrieved solar array. Liou et al. (2002) established an engineering model, ORDEM2000, to simulate the space debris environment. It incorporated in situ impact data from LDEF, HST solar array, EuReCa, Space Shuttle window and radiator, Space Flyer Unit and Mir. It covers a broad size range of orbital debris from 10 to 10 m. Paul (1995) summarized the impact damage according to the post-flight survey of LDEF and Berthoud and Paul (1997) observed the features of impact damage on the retrieved HST Solar arrays. Both of them provided useful information about the impact features of hypervelocity impacts from micrometeoroids Impact features The impact features show a large dependency on the target material. ESA (2006) divided it into two different types according to the target materials: ductile and brittle. Differences can be distinguished, but there are common features as well-either craters or holes. When impacting on a ductile material target, the crater or the hole is normally elliptical and surrounded by a raised lip due to the low hardness. Figure 4 shows a typical impact feature on a ductile aluminium plate. With respect to brittle material the impact features are more complex comparing with them on the ductile material. Around the central pit, there are always spall and fracture zones with a relatively considerable area compared with the size of the central crater.. Figure 5 shows a typical impact feature on a brittle material. 13

24 2. Literature review Figure 4 Hypervelocity impact on an aluminium plate (ESA, 2006) Figure 5 Hypervelocity impact on a brittle material (ESA, 2006) During the hypervelocity testing experiments and post-flight of retrieved space MMOD detectors several parameters are commonly measured as the characteristic dimensions. Figure 6 illustrates the definition of those different parameters, particularly relative to brittle targets. Several parameters are explained below in the following. Central crater (D p ) defines the major impact damage, usually with a raised lip. It is generally elliptical with a maximum and a minimum value. It applies to both ductile and brittle targets. Central hole (D h ) defines the size of the central hole when perforations occur. It applies to both ductile and brittle targets. 14

25 2. Literature review Conchoidal fracture zone (D co ) describes visible damage extent of an impact. Usually it happens when impacting on a brittle target, for example the cover glass of solar cells. In most cases it does not apply to ductile materials. Figure 6 Measured parameters of impacts on solar cell surfaces (ESA, 2006). In particular, Drolshagen et al. (1997) and Rival et al. (1997) gave a good description of damage features and impact morphology on solar cells, including small impacts, increasing craters and perforation holes Impact damage equations Damage due to impacts is usually evaluated using impact damage equations. They are usually developed empirically according to the experiments of hypervelocity impact shots. It is difficult to develop a uniform equation to cover all situations, because most empirically-developed equations are usually based on a limited set of experiment data. Typical materials used in spacecraft structure, such as MLI, aluminium, glass and composites, etc., are of particular interest to study and to carry out impact experiments. There are basically three different types of damage equations: semi-infinite equations for craters, marginal equations for critical perforation and finite equations with respect to perforation. A selection of damage equations are reviewed in this section. 15

26 2. Literature review McDonnell (1999) presented a set of damage equations with respect to the three categories, comprising 1. Ballistic limit equation, that gives the marginal target thickness corresponding to a certain size particle with some velocity. 2. Crater diameter equation, that gives the size of the crater on a semi-infinite thickness target. 3. Hole growth equation, that gives the size of the perforation hole on a thin/finite foil or plate, where particles may go though the target. The author compared the new-developed formula with former equations developed by other authors and they are applied to space data, and it is found that they are widely suitable for impact of meteoroids and debris on foil detectors and spacecraft surfaces. This is because the equations are developed from data with velocity up to 16 km/s. Lambert (1997) reviews experimental results regarding a broad range of materials, including aluminium, carbon-carbon, carbon fibre reinforced plastics, glass, multi-layer insulation and flexible external insulation, and summarized corresponding impact damage equations for different target materials developed by other authors and himself. Considerations and suggestions are given to hypervelocity impacts on Whipple shield and pressure vessels. Christiansen et al. (1997) developed several penetration equations to describe penetration damage particularly to thermal protection materials including low-density ceramic tiles, flexible ceramic insulation, multi-layer insulation, and reinforced carbon-carbon. They were developed based on the data collected from hypervelocity impact experiments carried by NASA Johnson Space Centre. Later the authors (Christiansen and Kerr, 2001) presented a set of ballistic limit equations delineating the protection capability of the shielding system. Kearsley et al. (2008) simulated dust impact on aluminium foils using different types of spherical projectiles and proposed a dimensional scaling law regarding the crater diameter and projectile diameter. Paul et al. (1997)reviewed the investigations results of impact sites found on retrieved solar panels of EuReCa and HST, and developed empirical damage laws. The equations are based on the data from the cover glass of solar cells, but can be applied to other similar materials. Hill (2004) identified an experimental formula relating the diameter of penetration hole to the hypervelocity impact with respect to the material properties and geometry characteristics of both 16

27 2. Literature review projectiles and target. Two different projectile shapes were studies separately, including spherical and cylindrical. Drolshagen (2001) summarized extensively the damage effects resulted from hypervelocity impacts on the spacecraft. In the paper several damage equations were presented including equations of penetration depth for single metal walls, equations for conchoidal spall crater diameter in semi-infinite glass targets, failure equation for perforations of a single metal wall, and equations for impact-generated plasma. Cour-Palais (1979) developed an empirical marginal equation for perforations regarding Apollo windows during NASA s lunar programme. 2.4 Spacecraft structure analysis In order to quantify the cumulative damage due to micrometeoroid impacts on spacecraft, it is necessary to provide a clear description of the object being studied. Among them the most important things are the orbit of the satellite, and the exposed structure to the micrometeoroid environment. In this paper a GEO communication satellite was presumed, and the fraction of its typical external surfaces is analyzed and quantified. Based on the experience gained from the development of space launches during the last five decades, assumptions are made that the typical size for a communication payload is 2.5m 2.5m 1m (L W H), that it is in GEO orbit, that it has a total mass of 2200 kg, and that the power that it needs to achieve the mission is 1700 W. The area of typical exposed surfaces is estimated afterwards, which are summarized in Table 1. The assumptions and estimations are based on the general empirically-trusted design rules and a typical communication spacecraft, TDRS that has been launched by NASA (Wertz and Larson, 2003). With respect to solar arrays the surface area required highly depends on the power that the spacecraft needs to maintain its operations. Empirically the solar array with current technology produces about 100 W/m 2 of projected solar cell area. While the area of MLI blanket simply depends on the area of the satellite/payload body, since it has to cover almost all the body surface. It is also determined using empirical formulas. Regarding radiators, their total exposed area could be calculated according to how much power it has to dissipate from internal electronic 17

28 2. Literature review boxes to outside space; in this case the assumed dissipating power of around W requires the total area of the radiators to be about 2 m 2. The antennas are also a big part of the surface exposed to the impacts of particles, especially for the communication satellite which requires high data rates. Here in the current case, two antennas are included in the design, and each has a diameter of 5m (used in TDSR). Then the total exposed area (front only) is about 39 m 2. Table 1 Summerization of typical spacecraft surface areas Typical surfaces Estimation formula Area (m 2 ) Solar arrays S solar = 0.01 P, where S solar is the 17 area of the solar array (m 2 ), and P is the total power (W). MLI S MLI =4L 2, 40 L=0.25M 1/3, where S MLI is the area of MLI (m 2 ), L is the linear dimension of the satellite (m), and M is the total mass of the satellite (kg). Radiators 2 Antennas S = 2 πr 2, where S is the area of antennas (m 2 ), and R is the radius of the antenna (m) Summary This chapter reviews most of the areas that are relevant to the study of interest in this project. Lots of research and studies have been done since the space era started, but more work still are necessary for humans to better understand the outside space. Section 1 presents the current space debris environment and meteoroid environment, which pose threats on space missions due to the possible hypervelocity impacts. Of particular importance are the micrometeoroid flux models, which are summarized and addressed in Section 2.2. It is critical to understand the interplanetary meteoroid flux to quantify the cumulative effects of their impacts on spacecraft. Section 2.3 reviews the phenomena of hypervelocity impacts generally and specifically in the area of space sector. Effects of impacts on spacecraft are summarized, and two types of ground-base testing facilities are introduced including Van De Graaff Accelerator and two-stage light gas gun, and some in situ impact experiments are also presented, and furthermore impact damage features and damage equations are introduced and summarized. Section 2.4 analyzes typical surfaces of spacecraft structures that are exposed directly to space environment. Taking a former satellite as an example, their area is estimated and quantified approximately. 18

29 3. Methodology 3. Methodology The problem of interest is the accumulation of micrometeoroid impacts on spacecraft surfaces. The subject of hypervelocity impact has been widely studied during the last several decades. However, the cumulative effects have rarely been evaluated and quantified, which is becoming increasingly necessary and imperative as the issues of space debris come into concern. 3.1 Single Impact Prior to quantifying the cumulative effects a good understanding of single impact mechanisms is essential. The impact morphology is greatly dependent on the particle impacting parameters and target mechanical properties. Among them the most important ones are size, density, and velocity of projectile, and the target material. M. Rival et al. (1997) generally classified the damage morphology into three categories: small impacts, increasing size craters, and perforations. Small impacts are defined when the target is thick compared with the size of impacting particles. As the impacting energy increases (larger and/or faster particles), the size of resultant craters becomes larger and larger. This phase is characterized as the increasing size craters. For more energetic impacts the whole target structure will be completely penetrated. The following question of interest is the relationship between the size of the crater/hole and the size of the impacting particle:, where is the diameter of either a crater or a hole, and is the diameter of the impacting particle, and is the velocity of the projectile. Here assumptions are made that the impacting particles are all spheres, and that the damage craters are hemi-spheres, and that holes are cylindrical. To simplify our long-term damage model the impact morphology is divided into either craters or holes (perforation) determined by ballistic limits, which could be derived from ballistic limit equations developed by former studies (McDonnell, 1999; Cour-Palais, 1979; Gardner et al., 1997; Pailer and grün, 1980). If the particle is energetic enough it will penetrate the target; hence the size of the hole is used to describe the damage feature. Otherwise the target is considered as a semi-infinite plate, and the size of the crater needs to be determined. 19

30 3. Methodology Since the sizes of micrometeoroids cover a wide range from g to 10 2 g (Grün et al., 1985) and typical spacecraft surfaces all have a limited thickness, small micrometeoroid particles will only cause craters on the surface of the spacecraft, while bigger ones will perforate it. Therefore, a critical parameter is the particle size at marginal perforation, which is determined by empirical marginal thickness f/d equations (ESA, 2006). In this paper the equation developed by Cour Palais (1979) is adopted, which is shown below in Eq Where f is the ballistic limit ( ) which is the thickness of target when a specific particle could just completely penetrate it, d mar is the marginal diameter of impacting particles ( ), is the density of the impacting particle (g/cm 3 ), and V is the impacting velocity (km/s). 3.2 Micrometeoroid flux To study the cumulative effects knowledge of the interplanetary micrometeoroid flux is of great importance, because it tells the number and magnitude of impacts that will occur during a certain period of time. Grün et al. (1985) developed an analytical micrometeoroid flux model which is still trusted in the science and engineering community. It was given as a function of mass of particles in a form as stated below,, where F is the cumulative flux per unit area due to particles with a mass m and greater onto a single-sided surface. However, when calculating cumulative area and mass flux, it is important to derive the derivative of the cumulative flux with respect to mass as F(m) = -df(m)/dm m = f(m) m It gives the contribution to the total cumulative flux by the particles within the mass range (m, m+dm). Since the evaluated orbit in this paper is GEO orbit which is nearly beyond the earth influence, the interplanetary micrometeoroid is of most concern. This means that there is not much contribution of man-made orbital debris to the particle environment in GEO. Another point is that the model of micrometeoroids shall be integrable. Therefore, the Grün et al. (1985) model, 20

31 3. Methodology which is analytically integrable and has been used in scientific community for almost 20 years, is adopted in the study. 3.3 Cumulative effects Here two new terms are defined: Volume Ejection Rate (VER) and Area Damage Rate (ADR). VER defines the rate of ejected target material volume due to impacts by micrometeoroids, while ADR describes the rate of growth of damaged area due to impacts. VER is more useful with respect to bulk mass such as Whipple shield plate, cover glass of solar cells which relatively have fewer perforations, while ADR is more useful regarding thin layers and surfaces with a high requirement of surface quality, such as multi-layer insulation and optical surfaces of space instruments. Both of the two terms are defined as parameters to describe cumulative damage effects of micrometeoroid impacts on spacecraft and can both be estimated based on the single impact mechanism and the analytical model of micrometeoroid flux. The formulas are given below in Eq. 3-2, Eq Results of VER and ADR can provide an estimate of the time scale for micrometeoroid impacts to erode away the bulk mass of spacecraft structure or to cover all the important surface areas Where is the mass of the impacting micrometeoroid particle, is the bulk volume ejected by the correspondent particles, is the damage area covered their impacts. and depend strongly on the target spacecraft structure, due to their different material properties and different geometry configurations. 21

32 4. Analysis of different exposed surfaces 4. Analysis of different exposed surfaces According to the methodology this chapter analyzes the correspondent single impact mechanisms and quantifies cumulative effects with respect to solar panel, multi-layer insulation and radiators respectively. 4.1 Solar Cells The solar panel surface area is a big part of the total spacecraft surface area exposed directly to the space environment, particularly the micrometeoroid impacts in this case. Hence the impacts on solar cells are worthwhile to investigate Solar cell structure Since the research is primarily based on data obtained from retrieved solar arrays of EuReCa and HST, their structures are investigated and adopted to further the study of hypervelocity impact effects. The configuration of solar cells that was used in HST is shown in Figure 7. The thickness of the cover glass on the top of solar cells is 150 µm. As far as this paper is concerned, the degradation of the cover glass is studied and quantified Single impact damage on solar cells To calculate the marginal particle size, assumptions are made that the multi-layer solar panel structure is reduced as a single layer of cover glass with the same thickness as the summation of all the layers, 600 µm. The material properties and geometry features of micrometeoroids and solar panel model is summarized in Table 2. Afterwards the marginal particle size is calculated using Eq.3-1, with a value of

33 4. Analysis of different exposed surfaces Figure 7 The structure of solar cells on EuReCa (ESA, 2006). Table 2 the material properties and geometry features of micrometeoroids and cover glass (ESA, 2006) Parameters Micrometeor oids Cover glass (Target) Mean velocity (km/s) Mean Impacting angle (degrees) Thickness ( ) Materials Velocity of Sound (km/s) Rock Density (g/cm 3 ) 600 Glass Particles with size smaller than generate craters on the cover glass, while particles with size bigger than will perforate a hole through the cover glass. The dimensions of craters and holes are determined by respective damage laws. Paul and Berthoud (1997) derived empirical scaling laws for solar cell impacts (Eq. 4-1, 4-2), which implemented the new factor of impacting angle and were calibrated by historic and newly obtained data and is currently considered as the 23

34 4. Analysis of different exposed surfaces most accurate formula with respect to semi-infinite target. Regarding perforation damage laws for predicting hole diameter in thin plates from hypervelocity impacts, Scott A. Hill (2004) proposed an empirical relationship based on a large amount of hypervelocity impact experiments. The equation is shown in Eq Where d co is the conchoidal cracking diameter, d c is the crater diameter, d h is the hole diameter, d p is the diameter of impacting particle, and are the target and particle density, is the velocity of impacting particle, is the impacting angle, and are the velocity of sound in the material of the particles and target respectively, and is the thickness of the target. All units are [cgs] Cumulative damage Since the Grün et al. flux model is valid in the mass range from to 10 2 (Grün et al., 1985), the same mass range of impacting micrometeoroids is taken into account for cumulative damage. From the last section, the marginal diameter ( ) of the impacting particles has been given as a value of, the integration interval is divided into two: one is from to in which these small particles only result in craters with a presumed hemisphere shape on the cover glass, the other one is from to 10 2 in which bigger particles will penetrate holes with a assumed cylinder shape on the bulk of cover glass. With these assumptions the VER and ADR are integrated over the whole micrometeoroids mass range. The calculation process and results are shown in Table 3. 24

35 4. Analysis of different exposed surfaces Table 3 Calculation process and formula of VER and ADR regarding the cover glass PAR Formula Results Where, VER ( ),, 1.35e-16,. ADR ( ) Where,,, 9.48e-13, Lifetime estimates Regarding the cover glass degradation due to micrometeoroid impacts, it is useful to know the timescale for how long it will take micrometeoroids to erode away all the cover glass mass or fracture the whole cover glass area. The formula to quantify the length of time is as stated below in Table 4. According to the results it can be seen that the timescale is about 10 4 years when the cover glass is eroded away or all the surface area is cracked solely due to micrometeoroid impact. Table 4 Formula to estimate lifetime of cover glass and results Terms Formula Results Volume ejection years Damage area coverage years 25

36 4. Analysis of different exposed surfaces 4.2 Multi-Layer Insulation (MLI) MLI is commonly used on satellites for thermal protection to reduce the heat loss by thermal radiation. It represents the typical surfaces of spacecraft bodies, giving them the appearance of being wrapped with gold foil. Therefore, it is valuable to study and quantify the cumulative effects of micrometeoroids impacting on it Structure of MLI The typical structure of MLI commonly used in space consists of a couple of layers of Kapton with separating Dracon nets as spacers in between. To reduce the conductive heat pass, the neighbouring layers only touch at a few points. The configuration is shown below in Figure 8, and composition details are shown in Figure 9. Note that the first layer (cover layer) is normally thicker than the following layers dues to the issues of impacts and erosion. In this paper we take 3 mil (75 ) as the thickness of the first layer. Figure 8 The typical structure of MLI (Turner et al., 2001). Figure 9 Detailed composition of a typical MLI blanket. (Wertz and Larson, 2003) 26

37 4. Analysis of different exposed surfaces Single impact on MLI Former studies have demonstrated the phenomena of a perforation cone through all the layers because of a shower of debris particles due to the fragmentation effect, when a hypervelocity particle impacts on the MLI blanket (Stadermann et al., 1997). However, since adjacent layers of MLI are separated, only impact damage to the first cover layer (75 ) is considered and quantified in order to simplify the impact model. The material properties and geometry features of micrometeoroids and 1 st layer of MLI blanket are summarized in Table 5. Afterwards the marginal particle size is calculated using Eq. 3-1, with a value of 4.8. It can be seen clearly that the marginal diameter of impact on MLI cover layer is fairly small, which indicated that perforations could easily occur on MLI. Until now there are very limited hypervelocity impact experiments of MLI have been executed, because the performance of MLI is insensitive to the perforations on it. No exactly matched scaling laws for the Kapton layer are available at the moment. Comprise is necessary, so Eq. 4-1, 4-2, 4-3 are still used in the single particle impact model regarding MLI blanket. Table 5 the material properties and geometry features of micrometeoroids and the first layer of MLI blanket. Parameters Micrometeor oids Mean velocity (km/s) Mean Impacting angle (degrees) Thickness ( ) Material Velocity of Sound (km/s) Density (g/cm 3 ) Rock st layer of MLI blanket (Target) 75 Kapton (Polymide)

38 4. Analysis of different exposed surfaces Cumulative damage Regarding cumulative damage of MLI, it is more reasonable to calculate the parameter ADR rather than VER, because the multiple layers of MLI blanket are so thin that they almost have no bulk volume and most of impacting particles are able to penetrate them due to a very small marginal diameter. Following the same calculation procedure with the case of the cover glass of solar cells, the integration interval is divided into two: one is from to in which these very small particles result in craters with a presumed hemisphere shape on the cover layer of the MLI blanket, the other one is from to 10 2 in which bigger particles will perforate it. The ADR is integrated over the whole micrometeoroid mass range. The calculation and results are shown in Table 6. Table 6 Calculation process and formula of ADR regarding the cover layer of MLI blanket PAR Formula Results ADR ( ) Where,,, 9.76e-13, Lifetime estimates Using the same formula with the one used in the section of cover glass, the lifetime is calculated and the value is years. Therefore it also takes a timescale of 10 4 years for micrometeoroid impacts to cover the whole surface area of MLI blanket. However, the difference of the cumulative damage between MLI blanket and the cover glass of solar cells can be expected that the cover layer of MLI blanket is more likely to be fragmented due to its thin thickness. 4.3 Radiator Waste heat generated by internal spacecraft is usually ejected to space by radiators. The area of the radiator depends on how much power needs to be dissipated. It is also a typical spacecraft 28

39 4. Analysis of different exposed surfaces surface with a considerable area exposed to the space environment. NASA found a clear evidence that micrometeoroid had penetrated a hole about 2.7 mm in diameter on one of the Atlantis orbiter s radiator panels (Oberg, 2006). Figure 10 shows the damage feature. Technicians discovered that the impacting particle completely perforated the 6 mm aluminium honeycomb panel. Accordingly it is of importance to investigate the damage effects of micrometeoroids impacting on the radiator surface. Figure 10 The hole observed on one of Atlantis orbiter s radiator panel (Oberg, 2006) Structure of radiator Basically the space radiator is a flat plate usually made of copper and with a coating of silvered or aluminized Teflon, which has high emissivity and low absorptivity to maximize the heat ejection rate and to minimize the heat flux from the Sun. As the coating layer is very thin, the structure of the radiator in this paper is just simplified as a copper plate. Typically its thickness is 0.18 mm (Haller and Lieblein, 1968) Single impact on radiator surface The material properties and geometry features of micrometeoroids and radiators are summarized in Table 7. Afterwards the marginal particle size is calculated using Eq. 3-1, with a value of Eq. 4-1, 4-2, 4-3 are still used as the scaling laws of single particle impact. 29